The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets

TL;DR

This paper introduces Richardson extrapolation with coarse regularisation parameters to significantly enhance the accuracy and efficiency of the regularized stokeslets method in microscale fluid dynamics, reducing computational costs.

Contribution

It demonstrates how Richardson extrapolation can be effectively applied to the regularized stokeslets method to lower costs and improve accuracy without sacrificing precision.

Findings

Order of magnitude improvement in accuracy and efficiency

Reduced storage and solution costs

Validated through numerical experiments on resistance and mobility problems

Abstract

The method of regularised stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly-varying regularised stokeslet kernel. Here we show how Richardson extrapolation with coarse values of the regularisation parameter is ideally-suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency.